A160917 Averages of twin prime pairs which can be represented as a sum of three consecutive of such pair averages.

60, 282, 348, 522, 570, 618, 1788, 2112, 4050, 4422, 5880, 6198, 8232, 9678, 10458, 11700, 12072, 12162, 12378, 14010, 16140, 17598, 17838, 21648, 22698, 33348, 36342, 39228, 41610, 43782, 44088, 46272, 48780, 51198, 53088, 56910, 58230

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, May 30 2009

Keywords

• nonn

Comments

Values A014574(j) of the form A014574(k)+A014574(k+1)+A014574(k+2).

Examples

			a(1) = 60 = A014574(7) = 12 + 18 + 30 = A014574(3) + A014574(4) + A014574(5).
a(2) = 282 = A014574(19) = 72 + 102 + 108 = A014574(8) + A014574(9) + A014574(10).
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harvey P. Dale)

Crossrefs

Cf. A014574, A160916, A160918.

Programs

Mathematica

PrimeNextTwinAverage[n_]:=Module[{k},k=n+1;While[ !PrimeQ[k-1]||!PrimeQ[k+1], k++ ];k];lst={};Do[If[PrimeQ[n-1]&&PrimeQ[n+1],a=n;b=PrimeNextTwinAverage[a]; c=PrimeNextTwinAverage[b];a=a+b+c;If[PrimeQ[a-1]&&PrimeQ[a+1],AppendTo[lst, a]]],{n,8!}];lst
Module[{m=Mean/@Select[Partition[Prime[Range[10000]],2,1],#[[2]]-#[[1]] == 2&],t},t=Total/@Partition[m,3,1];Intersection[m,t]] (* Harvey P. Dale, Mar 06 2018 *)

Extensions

Comments moved to the examples - R. J. Mathar, Sep 11 2009